Loss of mountain ice and earth rotation?

If mass is migrating to lower elevations, must be, days getting shorter. Like the spinning ice skater drawing in their arms. Next question is how much.

 

Enough for atomic clocks to detect over a year, already detected variances in the length of days

 

Wouldn't that depend on the location of the glacier or the ice that's melting and where it ends up? Seems like it would matter at least a little.

If I remove a billion tons of ice from the furthest north or south point on earth and drop it at the equator, wouldn't it slow the earth?

 

Earth spinning faster: shortest day in modern history recorded | verifythis.com

 

That depends on the latitude of the originating glacier.

When an equatorial mountain glacier melts, the mass necessarily moves closer to the spin axis, so the spin rate increases. But when a polar glacier melts and its mass gets spread somewhat evenly across the ocean's surface, it results in the mean mass getting moved farther away from the spin axis, slowing down the spin rate.

The 'balance point' latitude would be a nice calculus question. And of course, the 'balance point' would be a cylinder around the rotation axis, thus intersecting the surface at an angle, so would also be a (weak) function of initial elevation.

 

Yes, this is the best way to explain it, but the opposite is actually going on because most of the weight of glaciers is at the poles where there's far less centrifugal force involved.

The real problem we're having with Earth rotating slower is because 8 billion humans are creating water reservoirs just about everywhere which is akin to the figure skater spinning holding arms out (expand outside of rotation) to slow their spin. Even the world's largest dam on it's own was able to slow the earth's rotation by a measurable amount:



"NASA has calculated that the dam only slows the rotation by 0.06 microseconds, which is six hundredths of a millionth of a second. Our planet’s rotation speed actually fluctuates fairly often, as it can be influenced by earthquakes, the moon, and the climate change-induced movement of the North Pole." https://www.kinetica.co.uk/2014/03/27/chinese-dam-slows-down-earths-rotation/

 

Other information I've seen is that overall, very large human-built water reservoirs have actually sped up Earth's rotation, due to their mid-latitude locations. But this has been some orders of magnitude smaller than lunar tidal drag, with does gradually cause a slowing. I.e. overall, those reservoirs have just slightly slowed an inevitable natural change.

That lower-latitude Three Gorges Dam is being given credit for a slowdown of 0.000,06 milliseconds per day. For comparison, Wikipedia quotes a source:

"Atomic clocks show that a modern day is longer by about 1.7 milliseconds than a century ago,[1] ..."

Also ...

"Analysis of historical astronomical records shows a slowing trend; the length of a day increased about 2.3 milliseconds per century since the 8th century BCE."

... which amounts to a 64 millisecond slowdown since then, vastly greater than any anthropomorphic changes.

 

Just to put in context:

There's a thousand milliseconds in a second. So if the rate of slowing stays per the above quote, it'll take 1000/1.7*100 years for our length of day to increase one second: roughly 58,824 years.

 

... but put into an astronomical context, if that slowdown since the 8th century BCE happened at a steady rate, then it changed the timing of solar total eclipses by more than 5 minutes, completely changing the paths of solar totality.

Ancient Asian astronomical records are extremely useful for this.